SMPLNORM - A SIMPLE-MODEL FOR CALCULATING THE JOINT PROBABILITIES OF 2 FLOWS AND THE RELEVANT WATER-LEVEL

Most bivariate models assume the same type of marginal distribution, with two parameters, for two variables (gamma, type I extreme values, and so forth). The disadvantage of these models is that it is often difficult to make adjustments for observed flows. This study shows the application flexibility of a program that calculates the joint probability of two variables, Q1 and Q2, with marginal distributions that have three parameters. The program can also provide the probability of nonexceedence of a third variable, H, mathematically related to the first two variables. Two applications are discussed, in which Q1 and Q2 are the flows of two rivers controlling the variable H, which is a level in both cases. Theoretically, this model could also be applied to other types of variables. The proposed model is based on the hypothesis that a Box-Cox type of power transformation could reduce the marginal distributions of Q1 and Q2 to a normal distribution. One of the main conclusions of the study addresses the importance of taking into account the correlation between Q1 and Q2 to obtain a valid estimate of H.